Multiple generation systems feed into the same grid. If they're out of phase by even a few milliseconds, that translates to huge power losses. If power generation companies didn't synchronize to high precision, they would lose a lot of power and probably break some equipment.
The phases of the grid as a whole actually get synched up automatically. For example when they spin up a new turbine at a power plant if it is not within a certain percentage of the phase cycle it can actually cause massive amounts of damage as it gets pulled into the phase automatically.
The electric grid companies actually want to lower the current requirements for the 50/60 Hz cycle to be accurate in a 24 hour period to longer, such as possibly a week. This could mean that the clock in your oven for example may be a minute or two slow and slowly catch up over time as the grid has moments where it is clocked faster than 50/60 Hz.
For example see this graph of the last 60 minutes: http://www.nationalgrid.com/uk/Electricity/Data/Realtime/Fre... and here it is in real time for the whole US: http://fnetpublic.utk.edu/gradientmap.html
And here is the experiment that the power companies wanted to run/still are running regarding the relaxing of keeping the grid at 60 Hz: http://www.nbcnews.com/id/43532031/ns/technology_and_science...
https://www.entsoe.eu/publications/system-operations-reports...
It's actually a pretty elaborate system (who would have guessed?) with phase-stiffness between subsystems specified, because this basically defines the amount of power drawn/sourced. Timing is just the "outermost" regulation loop.
When I sailed on ships we knew not to use alarm clocks that plug into an outlet, because the load on the ship's generators is always changing, thus making plug-in alarm clocks less dependable than wrist watches.
Yes, the load changes the frequency over the course of a day. In Great-Britain there's even a special peak after the afternoon TV shows finishes and people start turning on their electric kettles to prepare tea.
http://www.bbc.co.uk/britainfromabove/stories/people/teatime...
In fact, the exact frequency of the power grid can be used to identify precisely the time of the day!
http://en.wikipedia.org/wiki/Electrical_network_frequency_an...
I can't immediately find a cite for the story that some enterprising electric clock company would give clocks to execs at power companies, then let them get annoyed at large errors and demand stable frequency, but that's surely too good to need a cite, eh?
(edit: initially imprecise)
The amount of power wasted is insane though. Bringing new turbines online for example means getting the turbine to run in sync with the current clock cycle within a certain percentage otherwise massive damage can be done as the turbine jumps backwards or forwards when connected to the grid.